sknano.core.geometric_regions.Parallelogram

class sknano.core.geometric_regions.Parallelogram(o=None, u=None, v=None)

Geometric2DRegion for a parallelogram.

New in version 0.3.0.

Represents a parallelogram with origin \(o=(o_x, o_y)\) and direction vectors \(\mathbf{u}=(u_x, u_y)\) and \(\mathbf{v}=(v_x, v_y)\).

Parameters:

o : array_like, optional

Parallelogram origin. If None, it defaults to o=[0, 0].

u, v : array_like, optional

Parallelogram direction vectors stemming from origin o. If None, then the default values are u=[1, 0] and v=[1, 1].

Notes

Parallelogram represents the bounded region \(\left \{o+\lambda_1\mathbf{u}+\lambda_2\mathbf{v}\in R^2 |0\le\lambda_i\le 1\right\}\), where \(\mathbf{u}\) and \(\mathbf{v}\) have to be linearly independent.

Calling Paralleogram with no parameters is equivalent to Parallelogram(o=[0, 0], u=[1, 0], v=[1, 1])

Attributes

area	Paralleogram area, \(A=|\mathbf{u}\times\mathbf{v}|\).
center	Alias for centroid.
centroid	Paralleogram centroid, \((c_x, c_y)\).
fmtstr	Format string.
measure	Alias for area, which is the measure of a 2D geometric region.
o	2D point coordinates \((o_x, o_y)\) of origin.
u	2D direction vector \(\mathbf{u}=(u_x, u_y)\), with origin o
v	2D direction vector \(\mathbf{v}=(v_x, v_y)\), with origin o

Methods

center_centroid()	Center centroid on origin.
contains(point)	Test region membership of point in Parallelogram.
rotate([angle, axis, anchor_point, ...])	Rotate GeometricRegion points and vectors.
todict()	Returns a dict of the Paralleogram constructor parameters.
translate(t[, fix_anchor_points])	Translate GeometricRegion points and vectors by Vector t.